Dynamical Systems and Chaos (ΕΜ5)
General
| School | School of Science |
|---|---|
| Academic Unit | Department of Mathematics |
| Level of Studies | Graduate |
| Course Code | EM5 |
| Semester | 1 |
| Course Title |
Dynamical Systems and Chaos |
| Independent Teaching Activities | Lectures (Weekly Teaching Hours: 3, Credits: 7.5) |
| Course Type | Special Background |
| Prerequisite Courses | - |
| Language of Instruction and Examinations | Greek |
| Is the Course Offered to Erasmus Students | Yes (in English) |
| Course Website (URL) | See eCourse, the Learning Management System maintained by the University of Ioannina. |
Learning Outcomes
| Learning outcomes |
The course is an introduction to continuous and discrete dynamical systems. Non linear systems of differential equations often lead to non-deterministic (stochastic) results and chaotic situations. The objectives of the course are:
Upon completion of the course the postgraduate student will be able to solve with analytical and numerical mathematical methods problems of the dynamical systems and to further deepen their understanding. |
|---|---|
| General Competences |
The course aims to enable the postgraduate student to:
All the above will give to the students the opportunity to work in an international multidisciplinary environment. |
Syllabus
Dynamical systems and differential equations of motion, Equilibrium points of the dynamical system, Period doubling of non-linear differential equations, Phase space of the dynamical system, Chaotic trajectory of the system, Poincare map, Applications of the dynamical systems, Henon map, Mandelbrot και Julia sets, Self-similarity under scale change and Fractals. The course includes training in computational methods in the computer laboratory (Applied and Computational Mathematics Laboratory).
Teaching and Learning Methods - Evaluation
| Delivery |
In class | ||||||||||
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| Use of Information and Communications Technology |
Use of computer lab (Applied and Computational Mathematics Laboratory). | ||||||||||
| Teaching Methods |
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| Student Performance Evaluation |
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Attached Bibliography
- Δυναμικά Συστήματα και Χάος, Πρώτος Τόμος, Α. Μπούντης, 1995, Εκδότης: Α. ΠΑΠΑΣΩΤΗΡΙΟΥ & ΣΙΑ Ι.Κ.Ε.
- Δυναμικά Συστήματα και Χάος, Δεύτερος Τόμος, Α. Μπούντης, 2001, Εκδότης: Εταιρεία Αξιοποίησης και Διαχείρισης Περιουσίας Πανεπιστημίου Πατρών.
- An Introduction to Dynamical Systems and Chaos, G.C. Layek, 2015, Editor: Springer.